## Darboux Transformations from n-KdV to KP (1997)

Venue: | Acta Applicandae Mathematicae |

Citations: | 6 - 4 self |

### BibTeX

@ARTICLE{Kasman97darbouxtransformations,

author = {Alex Kasman},

title = {Darboux Transformations from n-KdV to KP},

journal = {Acta Applicandae Mathematicae},

year = {1997},

pages = {179--197}

}

### OpenURL

### Abstract

Abstract. The iterated Darboux transformations of an ordinary differential operator are constructively parametrized by an infinite dimensional grassmannian of finitely supported distributions. In the case that the operator depends on time parameters so that it is a solution to the n-KdV hierarchy, it is shown that the transformation produces a solution of the KP hierarchy. The standard definitions of the theory of τ-functions are applied to this grassmannian and it is shown that these new τ-functions are quotients of KP τ-functions. The application of this procedure for the construction of “higher rank ” KP solutions is discussed. 1.